Question: Multiply the following complex numbers, marked as blue dots on the graph: $[5(\cos(\frac{11}{12}\pi) + i \sin(\frac{11}{12}\pi))] \cdot [2(\cos(\frac{1}{3}\pi) + i \sin(\frac{1}{3}\pi))]$ (Your current answer will be plotted in orange.)
Answer: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $5(\cos(\frac{11}{12}\pi) + i \sin(\frac{11}{12}\pi))$ ) has angle $\frac{11}{12}\pi$ and radius $5$ The second number ( $2(\cos(\frac{1}{3}\pi) + i \sin(\frac{1}{3}\pi))$ ) has angle $\frac{1}{3}\pi$ and radius $2$ The radius of the result will be $5 \cdot 2$ , which is $10$ The angle of the result is $\frac{11}{12}\pi + \frac{1}{3}\pi = \frac{5}{4}\pi$ The radius of the result is $10$ and the angle of the result is $\frac{5}{4}\pi$.